It is well known that in the deformation and failure process of rocks

a rock system will constantly readjusts its structure to resist the external pressure when it develops to an unstable crack propagation period. Thus

the cracks are gradually concentrated to a local area orderly; and the strain energy is continuously dissipated. The system will have an energy circulation with the negentropy flow that is produced and added by an external disturbing. At the same time

the entropy of the system

which shows the chaotic degree of the structure and energy

is decreased; meanwhile

the dimension of the system shows that the uniform degree of the structure and spatial distribution of energy is decreased too. The rock system is far from the equilibrium state in this period; and the failure process means a catastrophic process of the system entropy. Based on the realization which is discussed above

the paper derives an entropy equation which contains structural factors and energy distribution on the basis of testifying the uniform of strain energy distribution and structural block distribution mode. By giving an equilibrium analysis of the entropy equation

the bifurcation set shows the local catastrophe is obtained; so

the entropy fold catastrophic failure criterion shows a local failure of rocks is obtained. Meanwhile

the cusp-catastrophe represents the degree of order of rock structure by entropy equation is discussed; By finding the solution of the bifurcation set of a rock system

the bifurcation set is the integrated failure criterion which is shown the entropy catastrophe of a rock system.